On the maximum value of ground states for the scalar field equation with double power nonlinearity

TL;DR

This paper investigates the maximum value of positive solutions to semilinear elliptic equations with double power nonlinearities, using the Pohozaev identity to analyze the solution's behavior under known existence and uniqueness conditions.

Contribution

It introduces a method to evaluate the maximum value of solutions by examining a function derived from the nonlinearity, expanding understanding of solution bounds.

Findings

Maximum value of solutions characterized under certain conditions

Application of Pohozaev identity to bound solutions

Enhanced understanding of solution behavior for double power nonlinearities

Abstract

We evaluate the maximum value of the unique positive solution to semilinear elliptic equations with double power nonlinearities. It is known that a positive solution to this problem exists under some condition.Moreover, Ouyang and Shi in 1998 found that the solution is unique under the same condition. In the present paper we investigate the maximum value of the solution. The key idea is to examine the function defined from the nonlinearity, which arises from the well-known Pohozaev identity.